We all have our own opinions about which city is worth visiting.
In fact, I enjoy Bern more than Montreux.
One of the special attractions of Montreux is the Rochers-de-Naye. At 2042 meters, it might be within your tolerance zone.
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That link is from the SwissTopo map:
which certainly has more detail than most people want or need. But,it gives you altitudes.
The lake side promenade and Chateau de Chillon are also quite nice.
And, I was about to say that there is no "Old Town" in Montreux, but decided I'd better check. There actually is:
Up on a hill.
I've been to Montreux four or five times, with one 3 day stay for
a business meeting. We had our meeting at a lake side hotel,
and meals at lakeside in the summer were very pleasant. There are nice
places along the lakeside promenade where you can have a nice meal
wih a nice view.
Good French food.
So, I thought about why Montreux does not appeal to me.
I concluded it is that:
1.- I am comfortable with the German language, but not with French.
2.- It is too hilly for walking in any direction except parallel to the lake shore. Less so in the past; more so as my knees have gotten arthritic with age. I really like to wander a city.
3,- I get my lake experience on Lake Lucerne, which I know well. It is adifferent kind of lake, and appeals more to me.
Why do I like Bern, even if it is not on a lake ?
1- The city of Bern, although definitely not completely level, has a large and quite attractive Altstadt - Old Town. The arcaded streets, with shops and restaurants, are nice to wander through. A fair amount is level. You can walk through and moderately down hill to the Nydegg Bridge, overlooking the bear pits. Or, you can ride the #12 tram, which makes a couple of stops along the way.
2.- The Rosegarden is always a nice target for a walk. The views are nice from there, although it does require a short steep walk up a street and paved path to get there. You can also get to it by tram with a stop on the side away from the river and old town, but I recall you have to make at least one change. Of course, there is a restaurant up there.
3.- There are a couple of restaurants at the Nydegg Bridge which I enjoy. One - The Old Tram Depot- for reliable Swiss German food and beer, with a pleasant view of the city, and an excellent, tiny, and hard to get into (because it is always full) Brasserie across the street from the Old Tram Depot. It has an eclectic and sophisticated menu.
Snowman- a member of this forum - likes the Tram Depot, and is quite familiar with the city, if you want more recommendations.. Since he lives in Geneva,he has a both perspectives to consider.
4. - I tend to stop by Bern for a half day when I am within easy reach. Since I spend a lot of time in regions within easy reach of Bern by train, that is a significant factor. Montreux is a longer ride for me. I have to plan to be there, rather than deciding on the last minute on a rainy day.
Either choice could be nice, depending on your personal preferences.